The cut US-version by CBS/FOX Video has been compared to the BBFC-18 UK-DVD by HKL.
There was no violence removed from the US-version like in the German ones, but there was one long plot scene taken away. The soup-scene was cut, which is unfortunate, because it is very funny.
1 plot scene cut = 174 sec.1 "extra sequence" = +0.6 sec.

0:00:00 - 0:00:47.98In the US-version you see 27 seconds long more logos than in the UK-version. The ones there go from 0:00:00 - 0:00:21. They are different logos, too, this is irrelevant for this report, though.

0:00:48.02 - 0:02:38.46The opening credits are also designed differently from version to version, like in the other Bruce Lee films and also irrelevant for this report. The length of the credits is equally long in the two version. The UK-version shows the opening credits from 0:00:21 - 0:02:07.

0:02:38.49 - 0:02:39.89The credits fade one more second into the film in the UK version, so from 0:02:07 - 0:02:08. Again, irrelevant for this report, and just mentioned as a sidenote.

0:03:57 - 0:06:51The soup-scene was removed from the US-version. The cut takes place as the man tells Tang Lung (Bruce Lee): "Go right on in."
A cut takes place now in the US-version. You see Bruce Lee entering, then the rapid pan is shown in that version and you see Bruce Lee leaving the place.
In the UK-version you see Bruce Lee eating the soups (see images).
It is not clear for which reason this scene was removed, because even in the censored German 18+ version by UFA, the scene is contained.
174 sec.

0:03:57,87 - 0:03:58,37Here you see the rapid pan of the US-version, not found in the UK-version. The timecode relates to the US-version. This sequence would be pointless in the UK-version. It is made up of 15 frames, which is about 0.6 seconds.
+0.6 sec.